[EM] monotonicity and summability criteria

[Daniel Bishop]

Russ Paielli wrote:

> Russ Paielli 6049awj02-at-sneakemail.com |EMlist| wrote:
>
>> It occurred to me a while back that the two criteria may be 
>> equivalent. That is, if a method passes monotonicity, perhaps it must 
>> also pass summability, and vice versa. That's just a hunch. Can 
>> anyone prove (or disprove) it?
>
>
> Let me partially answer my own question. It just occurred to me that 
> summability cannot imply monotonicity because it says nothing about 
> how the final array sum is interpreted to determine the winner. 
> However, the converse could perhaps still be true. Does monotonicity 
> imply summability? 

No. A Median Ratings election in which ratings can be any real number 
between 0 and 1 passes monotonicity but fails summability.